Earth isotopic accretion modeling

Isotopic accretion modeling. As already discussed, the Earth accreted over a period of time and so defining the "age of the Earth" is not a particularly meaningful exercise. It may, however, be even more serious than this, and... 

Azbel, I. Ya., Tolstikhin, I. N. (1993) Accretion and early degassing of the Earth Constraints from modeling of Pu-U-Xe isotopic systematic. Meteoritics, 56, 609-21. 

These models produced a zoned Earth with an early metallic core surrounded by silicate, without the need for a separate later stage of core formation. The application of condensation theory to the striking variations in the densities and compositions of the terrestrial planets, and how metal and silicate form in distinct reservoirs has been seen as problematic for some time. Heterogeneous accretion models require fast accretion and core formation if these processes reflect condensation in the nebula and such timescales can be tested with isotopic systems. The time-scales for planetary accretion now are known to be far too long for an origin by partial condensation from a hot nebular gas. Nevertheless, heterogeneous accretion models have become embedded in the textbooks in Earth sciences (e.g.. Brown and Mussett, 1981) and astronomy (e.g.. Seeds, 1996). 

Heterogeneous accretion models for the formation of the Earth advocate the initial accretion of refractory, less-oxidized components that make up the bulk of the planet (some 50-80%), followed by the accretion of a lower-temperature, more oxidized component (e.g., perhaps comparable to carbonaceous chondrites). The overall nature of the initially refractory material is not well characterized, but it could have affinities to ordinary or enstatite chondrites. These two-component mixing models seek to reconcile the observational constraints from chemical and isotopic studies of the silicate Earth. As of early 2000s, we do not have sufficient data to identify in detail the nature of these two components of accretion if they existed. 

The origin of the components that were accreted to make up the planets is the subject of intense discussion. Chondrite-mixing models attempt to build the planets using known chondritic materials. These models are constrained by the mean densities, moments of inertia, and, to the extent that they are known, the bulk chemical and isotopic compositions of the planets. Mars and 4 Vesta can be modeled reasonably well by known types of chondritic material (Righter et al., 2006). However, the Earth seems to have formed, at least in part, from materials that are not represented in our collections of chondritic meteorites (see below). 

The W isotopic compositions of various terrestrial samples, chondrites, iron meteorites, basaltic achondrites, lunar samples, and Martian meteorites are expressed as deviations in parts per 104 from the value for the silicate earth (such as the W in a drill bit or chisel), which are the same as those of average solar system materials, represented by carbonaceous chondrites. These values are summarized in Fig. 8.9, from which it can be seen that early segregated metals such as the iron meteorites and metals from ordinary chondrites have only unradiogenic W because they formed early with low Hf/W. The time differences between metal objects segregated from parents with chondritic Hf/W are revealed by the differences in W isotopic compositions between each of the metal objects and chondrites. The Hf-W model ages of all these metals indicate that all of their parent bodies formed within a few million years, implying rapid accretion in the early history of the solar system. 

The observed noble-gas abundances and isotopic ratios on Venus are summarized in Tables 3 and 4. The helium mixing ratio is a model-dependent extrapolation of the value measured in Venus upper atmosphere, where diffusive separation of gases occurs. The main differences between Venus and Earth are that Venus is apparently richer in He, Ar, and Kr than the Earth, and the low " Ar/ Ar ratio of — 1.1 on Venus, which is —270 times smaller than on Earth. The low " Ar/ Ar ratio may reflect more efficient solar-wind implantation of Ar in solid grains accreted by Venus and/or efficient early outgassing that then stopped due to the lack of plate tectonics. Wieler (2002) discusses the noble-gas data. Volkov and Frenkel (1993) and Kaula (1999) describe implications of the " Ar/ Ar ratio for outgassing of Venus. 

The reason why nearly all such approaches yield similar apparent ages that postdate the start of the solar system by a few tens of millions of years is that there was a very strong U/Pb fractionation that took place during the protracted history of accretion. The U-Pb model age of the Earth can only be young if U/Pb is fractionated at a late stage. This fractionation was of far greater magnitude than that associated with any later processes. Thus it has left a clear and irreversible imprint on the and isotope... 

Figure 4 Lead isotopic modeling of the composition of the silicate Earth using continuous core formation. The principles behind the modeling are as in Halliday (2000). See text for explanation. The Held for the BSE encompasses all of the estimates in Galer and Goldstein (1996). The values suggested by Kramers and Tolstikhin (1997) and Murphy et al. (2003) also are shown. The mean life (t) is the time required to achieve 63% of the growth of the Earth with exponentially decreasing rates of accretion. The p, values are the 2 U/2°4pb of the BSE. It is assumed that the p of the total Earth is 0.7 (Allegre et ah, 1995a). It can be seen that the lead isotopic composition of the BSE is consistent with protracted accretion over periods of 102-10 yr.

Kramers J. D. (1998) ReconciUng siderophile element data in the Earth and Moon, W isotopes and the upper lunar age limit in a simple model of homogeneous accretion. Chem. Geol. 145, 461-478. 

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